Britain keeps plunging further back in time as yet another plank of the welfare state is removed. This month we just slipped back 46 years, to before Ken Loach's Cathy Come Home shocked the nation on the plight of homeless families. His film – about a family falling into ever worse housing, from caravan to hostel, until their children are taken into care – launched a change in the law that entered the national state of mind. From then on, the welfare state would house the vulnerable with nowhere else to go. Local authorities were given a legal obligation to take families in and find them social housing locally at an affordable rent. No longer.

As of this month, the government has quietly changed the law. All a council need do is find a private landlord anywhere with a one-year lease, and wash their hands of them thereafter. Families can be housed anywhere with an "affordable" rent, hundreds of miles away in districts where rents are cheap because jobs are non-existent. Wrench children out of schools, parents from their jobs, take families away from where they lived for generations without the means to pay train fares for visits home – all this breaks the social contract on housing. So do the deep cuts in housing benefit: this week, regulations were laid that will set off a catastrophic and chaotic exodus in April. There is no legal definition of an "affordable" rent, but most people might presume it should never eat into the absolute minimum the state provides to keep a family alive. Yet, even after families are exported, many of these "affordable" rents will leave them with virtually no money to live on. One estimate finds only Middlesbrough has rents low enough for a family with four children to pay up and still keep the sum unemployment benefits are supposed to provide for bare survival.

Meanwhile, many of these families won't be able to pay the 20% of council tax due in April. That will mean huge arrears for councils, with bailiffs bills adding to the cost. As local authorities increasingly panic about finding alternative distant housing for all who will soon be evicted, it becomes plain the government has no idea of the enormity of what it is unleashing.

The government likes to quote bizarre cases of families housed in £100,000 a year mansions: it emerges that there were just five of these temporary oddities. Using extreme examples, the government pledged to cut the £20.8bn housing benefit bill by £2bn; instead it has already risen by £4.7bn. Almost all new claimants are in work – but earning too little to pay the rent: they will lose their jobs when forcibly removed elsewhere. The threat to make under-25s ineligible for housing benefit, forcing them to stay at home if they have one, will stop them leaving to seek apprenticeships or jobs after college: forget "on your bike" or social mobility – those born in workless Knowsley or Hull can never leave. MPs already have terrible stories. London MP Karen Buck tells of a father who gave up work when social workers brought him his four children because of his ex-wife's mental illness. Now he has been told to leave the home they gave him, a basic ex-council flat in a rundown estate, as the council sends them to cheaper Manchester, without schools or contacts.

Richest areas purged of all poorer residents no longer need share the national cost of caring for them, while lower-rent councils pick up the whole social bill. With some relish, councils heard Bournemouth MP Tobias Ellwood's shocked complaint that London councils were sending hundreds of "undesirable characters" on housing benefit to Bournemouth. Tory as well as Labour areas will face an influx of families needing schools, health and social services. But, as one Labour MP put it sourly: "They voted for this; let them see the consequences."

The government inherited a severe housing shortage: Labour failed to build, too. But cutting housing benefit turns a shortage into a crisis. Social housing is shrinking, while the cost of renting or buying is well beyond the reach of growing numbers. As the squeeze worsens, rents are rocketing, up by 4.3% last year, up by a third in three years in London. As people can't pay, landlord evictions have risen by 70%. Slum landlords are back: 42% of tenants are in sub-standard properties. Labour promises regulation. Rent controls are needed too.

Housing was always the prime example of market failure. Neither Beveridge nor anyone else has made rent fit any social security system. But this intensely ideological government refuses to believe markets can't solve everything: they assume housing benefit cuts must make rents fall. But there is no sign of it: rents rise and landlords turn away housing benefit tenants. The only way people can be tolerably housed is by governments building decent social homes, as Harold Macmillan and Labour did years ago. Or else the money can be shifted to subsidise tenants' private rents, as the Tories did in the 1990s when Sir George Young, housing minister, decreed: "Let housing benefit take the strain." This government is experimenting with doing neither.

Instead it pretends. Nick Clegg offered another fantasy yesterday when he "announced" a new era of garden cities, at a tiny £225m price. Compare that with the £4.5bn Osborne cut from house-building. His "new homes bonus" – to get cash-strapped councils to build – has failed. The £10bn of guarantees to get pension funds to invest in rental property falls on deaf ears: too risky for them. A year ago Cameron declared "a new Tory housing revolution", but in the last year new home starts fell by 9%. As the dysfunctions of the housing market infect every aspect of the economy, Labour looks set to make a huge building programme the centrepiece of its economic stimulus plan: some expect Jack Dromey's plan for 100,000 homes to be multiplied by 10.

If George Osborne tightens the housing benefit screw again next month, councils of every political hue must protest: they know the cataclysm that is already starting to happen. Housing associations fear a wave of rent arrears may bankrupt them. The epic scale of the crisis now unfolding is only just dawning on some: most of the public may not see it until late next year.